102 of all the Smiths,

If you are a Londoner and you have three initials, therefore, the chances of your initials being M.A.B. in that order are approximately 0.102 X 0.073 0-095 or about 0.0007. Since the population of Britain is 55 million, this should mean that about 38,000 of them have the initials M.A.B., but only if everybody among those 55 million has three initials. Obviously not everybody does but, looking down the telephone directory again, it seems that at least a majority do. If we make the conservative assumption that only half of British people have three initials, that still means that more than 19,000 British people have identical initials to my wife's mother. Any one of them could have bought that watch and gasped with astonishment at the coincidence. Our calculation has shown that there is no reason to gasp.

Indeed, when we think harder about the petwhac, we find that we have even less right to be impressed. M.A.B. were the initial letters of my wife's mother's maiden name. Her married initials of M.A.W. would have seemed just as impressive had they been found on the watch. Surnames beginning with W are nearly as common in the telephone book as those beginning with B. This consideration approximately doubles the petwhac, by doubling the number of people in the country who would have been deemed, by a coincidence hunter, to have 'the same initials' as my wife's mother. Moreover, if somebody bought a watch and found it to be engraved not with her mother's initials but with her own, she might consider it an even greater coincidence and more worthy to be embraced within the (ever-growing) petwhac.

The late Arthur Koestler, as I have already mentioned, was a great enthusiast of coincidences. Among the stories that he recounts in The Roots of Coincidence (1972) are several originally collected by his hero, the Austrian biologist Paul Kammerer (famous for publishing a faked experiment purportedly demonstrating the 'inheritance of acquired characteristics' in the midwife toad). Here is a typical Kammerer story quoted by Koestler: On September 18, 1916, my wife, while waiting for her turn in the consulting rooms of Prof. Dr J. v. H., reads the magazine Die Kunst; she is impressed by some reproductions of pictures by a painter named Schwalbach, and makes a mental note to remember his name because she would like to see the originals. At that moment the door opens and the receptionist calls out to the patients: 'Is Frau Schwalbach here? She is wanted on the telephone.'